Question

Which three measurements could be the length of a side of a triangle?

a. 25 ft, 30 ft, 60 ft
b. 40 ft, 60 ft, 70ft
c. 40 ft, 175, 220 ft
d. 80 ft, 150 ft, 230 ft

Answer 1

Upon the application of the triangle inequality theorem, only Option b, with side lengths of 40 ft, 60 ft, and 70 ft, satisfies the conditions to form a triangle, as the sum of any two sides is greater than the length of the third side.

Step-by-step explanation:

The question involves determining which of the given sets of measurements could represent the lengths of the sides of a triangle. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this theorem to each option:

• Option a: 25 ft + 30 ft = 55 ft, which is not greater than 60 ft, so these cannot be the sides of a triangle.
• Option b: 40 ft + 60 ft = 100 ft, which is greater than 70 ft, and the other combinations (40 ft + 70 ft and 60 ft + 70 ft) are also greater than the third side, so these could be the sides of a triangle.
• Option c: 40 ft + 175 ft = 215 ft, which is not greater than 220 ft, so these cannot be the sides of a triangle.
• Option d: 80 ft + 150 ft = 230 ft, which is equal to the third side, so these cannot be the sides of a proper triangle since one requirement (strictly greater) is not met.

Therefore, the measurements that could be the sides of a triangle are 40 ft, 60 ft, and 70 ft as listed in Option b.